Modeling three-dimensional groundwater flows by the body-fitted coordinate (BFC) method
Abstract
The purpose of this research was to determine if the body-fitted coordinate (BFC) method could be utilized to model three-dimensional groundwater flows and what advantages it offers. This method was initially developed and used in aerodynamics and heat transfer areas to simulate air and heat flows in irregular domains. Chapter 1 introduces the BFC method as an alternative to two popular numerical techniques, the finite difference method and the finite element method. In the first section of Chapter 2, coordinate transformation relations are described to assist in transforming partial differential equations used in the next two chapters. In the second section, numerical grid generation techniques are discussed, and some examples of body-fitted grids are illustrated. Chapters 3 and 4 show how to use the BFC method to solve three-dimensional groundwater flow equations. Chapter 3 describes methodology and solution procedure of the BFC method for simulating confined aquifer flows whose boundaries are fixed with time. Coordinate transformation of the governing equation and various boundary conditions is described. A three-dimensional finite difference computer code BFC3DGW was developed and verified by comparing numerical results to analytical solutions for well-flow problems in an isosceles right triangular aquifer. An example simulation was made to demonstrate capability of the code solving flow problems in anisotropic aquifers where directions of anisotropy change continuously. Chapter 4 shows how to apply the method to the solution of groundwater flow problems in unconfined aquifers whose boundaries are moving with time. Time-dependent coordinate transformation of the governing equation and the moving boundary condition is described. The developed code BFC3DGW was extended in such a way that it can deal with the time-dependent BFC system and the moving boundary condition. The code was used to solve two unconfined flow problems, transient free-surface seepage flow in a dam and well-flow in an unconfined aquifer. Difficulties associated with the free and moving boundary were successfully overcome by employing the BFC method. This method differs from the conventional finite difference method (FDM) in the ability to use a flexible, nonorthogonal, and body-fitted grid. The main advantages of the method are the convenience of grid generation and the simplified implementation of boundary conditions. The most attractive feature of the method is the capability to construct a generalized computer code which can be consistently applied to problem domains of any shape.
Degree
Ph.D.
Advisors
Leap, Purdue University.
Subject Area
Hydrology|Geology|Environmental science
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